As an opposite end surface truing tool used in an opposite end surface truing device for truing grinding surfaces at opposite ends of a grinding wheel, there has been known one wherein cylindrical truing sections each having diamond abrasive grains bonded thereon with a metal-base bond material (metal bond) are coaxially fixed on the external surface of a disc-like base rotatable about a rotational axis, as described in Japanese Unexamined, Published Patent Application No. 8-90411. As shown in FIGS. 2 and 3 of the Patent Application No. 8-90411, the opposite end surface truing tool is constructed to protrude the cylindrical truing sections 38, 39 each rectangular in cross-section from opposite end surfaces at circumferential portions of the base 36, and a wheel truing tool 35 as the opposite end surface truing tool is used to be mounted on the opposite end surface truing device with the rotational axis O2 thereof being inclined (inclination angle: 8 degrees for example) relative to the rotational axis O1 of a grinding wheel 21 which is provided with a grinding wheel layer 23 on the external surface of a grinding wheel core 22. The truing of a grinding surface 23b on one end of the grinding wheel layer 23 of the grinding wheel 21 with the second truing section 38 of the wheel truing tool 35 is carried out as indicated by the two-dot-chain line 21B in FIG. 3 by moving the wheel truing tool 35 in a Z-direction to infeed the second truing section 38 against the grinding surface 23b and then by moving the wheel truing tool 35 toward the rotational axis O1 in an X-direction, while the truing of a grinding surface 23c on the other end with the third truing section 39 is carried out as indicated by the solid line 21C in FIG. 3 by moving the wheel truing tool 35 in the Z-direction to infeed the third truing section 39 against a grinding surface 23c and then by moving the wheel truing tool 35 toward the rotational axis O1 in the X-direction.
In the foregoing prior art technology, since the spaces among the diamond abrasive grains are filled with the metal bond in a state that pores do not open, the diamond abrasive grains and metal bond at each of the truing sections 38, 39 become even in height, so that the diamonds not protruding cannot be cut into the grinding wheel sufficiently. Further, because the diamond abrasive grains are only mechanically embeded in the metal bond, but not joined chemically, the retention force for the abrasive grains is weak, and the diamond abrasive gains are easy to fall off the metal bond, thereby resulting in a decrease in the number of the abrasive grains which work to true the grinding surfaces 23b, 23c at the opposite ends of the grinding wheel 21. After trued with the wheel truing tool 35, the grinding surfaces 23b, 23c of the grinding wheel 21 become flat and dull, and where used for grinding, the grinding wheel 21 causes the grinding resistance to increase and is unable to secure the grinding efficiency and the surface quality as desired.
Further, the grinding surfaces 23b, 23c at the opposite ends are flat, and by inclining the rotational axis of the wheel truing tool 35 relative to the rotational axis of the grinding wheel 21, the edge portions of the truing sections 38, 39 at the opposite ends of the wheel truing tool 35 are made to contact with the grinding surfaces 23b, 23c at arc shapes. However, the contact length of each truing section 38, 39 with the grinding surface 23b, 23c is elongated to increase the truing resistance, so that it is unable for the diamond abrasive grains at each truing section 38, 39 to sufficiently crush CBN abrasive grains on each grinding surface 23b, 23c. 
Furthermore, because the wheel truing tool 35 is constituted to protrude the cylindrical truing sections 38, 39, made by binding diamond abrasive grains with the metal bond, from opposite end surfaces at the circumferential portions of the base 36 in the axial direction of the rotational axis, it is impossible from the standpoints of manufacturing and strength to make the depth in radial direction of each cylindrical truing section 38, 39 thin. This makes the contact area of each truing section 38, 39 with the grinding surface 23b, 23c large to increase the truing resistance, so that each grinding surface 23b, 23c cannot be trued sharply.
Furthermore, a research has been made of forming the second and third truing sections 38, 39 by bodily protruding cylindrical bodies from the opposite end surfaces of the base 36 in the axial direction and by binding diamond abrasive grains on the external surface of each cylindrical body as one layer or a thin layer. However, when the third truing section 39 of the opposite end surface truing tool is used to true the grinding surface 23c at the other end of the grinding wheel 21, the cylindrical body comes into contact with the grinding surface 23c earlier than the diamond abrasive grain layer does. This causes the truing resistance to increase and the diamond abrasive layer to lack the rigidity against the truing resistance for the reason of being not backed up by the base body, so that it is unable to true the grinding surface 23c into a sharp grinding surface having moderate ruggedness.
The present invention solves the foregoing programs and is designed to make it possible that grinding surfaces at opposite ends of a grinding wheel can be trued under almost the same condition into sharp grinding surfaces having moderate ruggedness.